Search results

* links to "rational number" and "polynomial"

...tive operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associat

Value <math>\ g(x)</math>&nbsp; is a rational number whenever ''x'' is rational. For instance, for ''x'' = &frac12;:

...(by computer) that verified, however, that zeta(3)/pi^3 doesn't equal any rational number whose numerator or denominator has less than 500 digits. I'm sure this sort

* The [[rational number]]s as a [[subspace]] of the [[real number]]s with the Euclidean metric topo

* The [[rational number]]s form an ordered field in a unique way.

...yle k = 1, \ldots, 13 </math>. In each case, he found that the value is a rational number times <math> \scriptstyle \pi^{2k} </math> Later, he discovered a general

# The [[rational number]]s (<math> \scriptstyle \mathbb{Q} </math>) are any number that can be repr ...2}</math> are both irrational. This set does not share any member with the rational number set.

...tably compact]]. But '''R''' is [[separable space|separable]] since the [[rational number]]s '''Q''' form a [[countability|countable]] [[dense set]], and this applie

...se "ordinary" integers, embedded in the [[field (mathematics)|field]] of [[rational number]]s, from other "integers" such as the [[algebraic integer]]s. ...ics)|field]]. The smallest field containing the integers is the field of [[rational number]]s. This process can be mimicked to form the [[field of fractions]] of any

...of [[mathematics]]. It studies the approximations of [[real number]]s by [[rational number]]s. This article presents an elementary introduction to diophantine approxi ...o this end we will not worry about the details of the difference between a rational number and a fraction (with integer numerator and denominator)&mdash;this will not

A real number may be either [[rational number|rational]] or [[irrational number|irrational]]; either [[algebraic number|a ...94) completed the proof, and showed that &pi; is not the square root of a rational number. [[Paolo Ruffini|Ruffini]] (1799) and [[Niels Henrik Abel|Abel]] (1842) bot

**The [[rational number|rational]], [[real number|real]] and [[complex number|complex]] numbers eac

...ation <math>x^2=2</math> has no solutions if the domain is formed by the [[rational number]]s, it has two solutions (namely, <math>x=\sqrt{2}</math> and <math>x=-\sqr

...le about a "real number" (something along the lines of "a real number is a rational number, or a mathematically consistent description of how a new number would be la

...problem with polynomials over rings of usual numbers like [[integer]]s, [[rational number|rational]], [[real number|real]] or [[complex number|complex]] numbers. Sti

...gree [[field extension]] of the [[field (mathematics)|field]] '''Q''' of [[rational number]]s. The elements of ''K'' are thus [[algebraic number]]s. Let ''n'' = [''

...ps. These include familiar number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s under addition, as we Consider the set of [[rational number]]s '''Q''', that is the set of numbers ''a''/''b'' such that

...s of a whole object, if the object is divided into five equal parts. Any [[rational number]] can be written as a fraction.

is a fixed rational number whose square root is not rational.)